| Major Topics on this Page | ||
| 7.1 | Mechanistic Model | |
| 7.2 | Failure Criteria | |
| 7.3 | A Mechanistic Computer Program | |
Mechanics is the science of motion and the action of forces on bodies. Thus, a mechanistic approach seeks to explain phenomena only by reference to physical causes. In pavement design the phenomena are the stresses, strains and deflections within a pavement structure, and the physical causes are the loads and material properties of the pavement structure. The relationship between these phenomena and their physical causes is typically a mathematical model. Various mathematical models can be (and are) used; the most common is a layered elastic model.
The empirical portion of a mechanistic-empirical approach comes about when defining what value of the calculated stresses, strains and deflections result in pavement failure (the point at which the pavement is no longer serviceable). This relationship between physical phenomena and pavement failure is described by empirically derived equations that compute the number of loading cycles to failure.
The basic advantages of a mechanistic-empirical pavement design method over a purely empirical one are:
This section describes the basics behind rigid pavement mechanistic-empirical design.
Mechanistic models are used to mathematically model pavement physics. There are different types of models available today (e.g., dynamic, viscoelastic models) but this section will present two, the layered elastic model and the finite elements model (FEM), as examples of the types of models typically used. Both of these models can easily be run on personal computers and only require data that can be realistically obtained.
A layered elastic model can compute stresses, strains and deflections at any point in a pavement structure resulting from the application of a surface load. Layered elastic models assume that each pavement structural layer is homogeneous, isotropic, and linearly elastic. In other words, it is the same everywhere and will rebound to its original form once the load is removed. Layered elastic models for rigid pavement use the same principles as those for flexible pavements. To read the layered elastic discussion, see Section 4.1.1, Layered Elastic Model.
The finite element method (FEM) is a numerical analysis technique for obtaining approximate solutions to a wide variety of engineering problems. Although originally developed to study stresses in complex airframe structures, it has since been extended and applied to the broad field of continuum mechanics (Huebner et al., 2001). In a continuum problem (e.g., one that involves a continuous surface or volume) the variables of interest generally possess infinitely many values because they are functions of each generic point in the continuum. For example, the stress in a particular element of pavement cannot be solved with one simple equation because the functions that describe its stresses are particular to its specific location. However, the finite element method can be used to divide a continuum (e.g., the pavement volume) into a number of small discrete volumes in order to obtain an approximate numerical solution for each individual volume rather than an exact closed-form solution for the whole pavement volume. Fifty years ago the computations involved in doing this were incredibly tedious, but today computers can perform them quite readily.
Much of the discussion in this section is identical to that of Section 4.1.2, Finite Elements Model (the flexible pavement FEM). However, this section uses EverFE, a FEM developed at the University of Washington for the Washington State DOT and U.S. Army Corps of Engineers by Davids, Turkiyyah and Mahoney (1998). As in flexible pavements, the FEM analysis of a rigid pavement discritizes the region of interest (the pavement and subgrade) into a number of elements with the loads at the top (see Figure 6.15).
Figure 6.15: EverFE Sample Deflection Display Showing Discretized Region of Interest
The FEM approach works with a more complex mathematical model than the layered elastic approach so it makes fewer assumptions. Generally, FEM must assume some constraining values at the boundaries of the region of interest. Additionally, the choice of element geometry (size and shape) as well as interpolation functions will influence overall model performance.
The typical finite elements method approach involves the following seven steps (Huebner et al., 2001):
Figure 6.16 shows a screen shot of one EverFE input screen.
Figure 6.16: EverFE Sample Input Screen
The outputs of a FEM analysis are the same as for a layered elastic model:
In addition, the finite elements method allows for extremely powerful graphical displays of these values (see Figures 6.12 through 6.14).
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| Figure 6.17: Input Screen (Plan View) | Figure 6.18: Stress View | Figure 6.19: Deflection View |
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Screen Shot Thumbnails from EverFE (Davids, Turkiyyah and Mahoney, 1998). EverFE is a project under development at the University of Washington. The project is supported by the Washington State Department of Transportation. Additional support is provided by the US Army Corps of Engineers. Click on each thumbnail to see a larger version of the picture. |
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The main empirical portions of the mechanistic-empirical design process are the equations used to compute the number of loading cycles to failure. These equations are derived by (1) determining the various stresses present in a rigid pavement section or slab, (2) observing the performance of pavements, and (3) relating the type and extent of observed failure to an initial stress under various conditions. These stress calculations are then tied to pavement performance using empirically derived relationships (often called transfer functions).
